Euclid-proof

Synthetic a priori Judgments and Geometry

In the Prolegomena, Kant uses geometry as an example to show that we do have synthetic a priori knowledge. He argues that grasping how this kind of knowledge is possible there can lead to insights concerning the possibility (and the limits) of synthetic a priori knowledge in other areas, such as metaphysics. We will focus…

P._Oxy._I_29 (1)

Descartes and Geometrical Demonstration

Reproduction of a proof from Euclid’s Elements (Public Domain: via Wikipedia Commons)   Those long chains of utterly simple and easy reasonings that geometers commonly use to arrive at their most difficult demonstrations had given me occasion to imagine that all the things that can fall within human knowledge follow from one another in the…